Abstract
This paper provides geometric insight into the duality between the kinematics of epicyclic gear trains and the statics of beam systems. The two devices have inherent geometrical relationships that allow the angular velocities of the gears in a gear train to be investigated from a knowledge of the forces acting on the dual beam system, and vice-versa. The primary contribution of the paper is the application of this duality to obtain the dual beam system for a given compound epicyclic gear train. The paper develops a systematic procedure to transform between the first-order kinematics of a gear train and the statics of the dual beam system. This provides a simple and intuitive approach to study the speed ratios of an epicyclic gear train and the force ratios of the dual beam system. The speed ratios are expressed in terms of kinematic coefficients, which are a function of the position of the input gear and provide insight into the gear train geometry. Several numerical examples of simple and compound epicyclic gear trains are presented to demonstrate the simplicity of the proposed approach. The analytical equations that are developed in the paper can be incorporated, in a straightforward manner, into a spreadsheet that is oriented towards an epicyclic gear train satisfying specific design requirements.
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